Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √222 + 262 - 2·22·26·cos(120°)
= √484 + 676 - 1144·-0.5
= √1732
= 41.62
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(120°))
= arcsin(0.5286·0.866)
= 27.24°
или:
α° = arccos(
)
= arccos(
)
= arccos(
)
= 27.24°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(120°))
= arcsin(0.6247·0.866)
= 32.75°
Периметр:
P = a + b + c
= 22 + 26 + 41.62
= 89.62
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√44.81·(44.81-22)·(44.81-26)·(44.81-41.62)
=√44.81 · 22.81 · 18.81 · 3.19
=√61330.95225279
= 247.65
Высота :
ha =
=
= 22.51
hb =
=
= 19.05
hc =
=
= 11.9